When I look at the UpDraftPlus settings (latest version) there is a long list next to Last backup job done and each item in the list says: Warning: A zip error occurred - check your log for more details. What's this all about?
Thanks!

That's a different log file from the one that has the original message in. Click on the big "Restore" button and try to locate the log file that corresponds to the backup that was running when you got the message.

David, is there typically anything contained in the complete log file that should make me skeptical about posting the whole thing here? There appears to be some hosting info that makes me a little worried...or should I relax and Pastebin it?

Yes, it'll contain some info about the hosting setup. It'd be 'interesting' to a hacker (background info), but not directly useful. Also, if you're with a public web hosting company, they could get the info through other means cheaply/easily.

Overdogart: When I click that link, it says: "This paste has been removed!"

philmcdonnell: I think your hosting company has something that kills off zip processes after 15 seconds. Stick this in your wp-config.php to enforce use of a different zip method to prevent the problem:

That line was for philmcdonnell - but the data is useful anyway. Yours now shows a different but related problem, that I have an idea for dealing with. Your backup looks fine, but it'd be better if we could eliminate the warning. I will get back to you.